Write a sum of three radicals that contains two like terms, algebra homework help

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.

1. OPEN ENDED Write a sum of three radicals that contains two like terms. Explain how you would combine the terms. Defend your answer.
2. Writing in Math Refer to the information on page 435 to explain how rational exponents can be applied to astronomy. Explain how to write the formula in radical form and simplify it. (find page 435 attached)
3. Writing in Math Refer to the information on page 442 to describe how the cost and the number of units manufactured are related. Rewrite the manufacturing equation C = 10n2/3 + 1500 as a radical equation, and write a step-by-step explanation of how to determine the maximum number of chips the company could make for $10,000 (.find page 442 attached)

7-6
Rational Exponents
Main Ideas
• Write expressions
with rational
exponents in radical
form and vice versa.
• Simplify expressions
in exponential or
radical form.
GET READY for the Lesson
Astronomers refer to the space
around a planet where the planet’s
gravity is stronger than the Sun’s as
the sphere of influence of the planet.
The radius r of the sphere of
influence is given by the formula
(MM)
r=D
M
where My is the mass
of the planet, M, is the mass of the
Sun, and D is the distance between the planet and the Sun.
Rational Exponents and Radicals You know that squaring a number
and taking the square root of a number are inverse operations. But how
would you evaluate an expression that contains a fractional exponent
such as the one above? You can investigate such an expression by
assuming that fractional exponents behave as integral exponents.
(69)? = b. b)
Write the square as multiplication.
= bż + Ź
Add the exponents.
= b1 or b Simplify.
1
1
Thus, bā is a number whose square equals b. So b2 = Vb.
1
bn
KEY CONCEPT
Words For any real number b and for any positive integer n, bħ= vb,
except when b< 0 and n is even. Example 83= or 2 EXAMPLE Radical and Exponential Forms 1 a. Write a 4 in radical form. b. Write Vy in exponential form. a) = vā Definition of bă Vy 1 = y; Definition of bi CHECK Your Progress 1B. VC 1A. x Lesson 7-6 Rational Exponents 415 7-7 Solving Radical Equations and Inequalities GET READY for the Lesson Main Ideas • Solve equations containing radicals. • Solve inequalities containing radicals. Computer chips are made from the element silicon, which is found in sand. Suppose a company that manufactures computer chips uses the formula C = 10n3 + 1500 to estimate the cost C in dollars of producing n chips. This can be rewritten as a radical equation. New Vocabulary radical equation extraneous solution radical inequality Solve Radical Equations Equations with radicals that have variables in the radicands are called radical equations. To solve this type of equation, raise each side of the equation to a power equal to the index of the radical to eliminate the radical. It is very important that you check your solution. Sometimes you will obtain a number that does not satisfy the original equation. Such a number is called an extraneous solution. EXAMPLE Solve Radical Equations Solve each equation. a. Vx+1+2 = 4 Vx + 1 + 2 = 4 Original equation Vx + 1 = 2 (Vx+1)2 = 22 Square each side to eliminate the radical. Subtract 2 from each side to isolate the radical. x+1=4 Find the squares. x= 3 Subtract 1 from each side. CHECK V x + 1 + 2 = 4 Original equation V3+1 +224 Replace x with 3. 4= 4 Simplify. The solution checks. The solution is 3. b. Vx – 15 = 3 – VX V x – 15 = 3 – VX Original equation (Vx – 15)2 = (3 – Væ)2 Square each side. X – 15 = 9 – 6VX + x Find the squares. -24 = -6vx Isolate the radical. Divide each side by - 6. 4=vx 42 = (Vx)? Square each side again. 16 = x Evaluate the squares.